Europhys. Lett, 47 (4), pp. 421-427 (1999)
Localization in a nonlinear disordered system
K. Ø. Rasmussen 1, D. Cai 2, A. R. Bishop 1 and N. Grønbech-Jensen 1
1 Theoretical Division, Los Alamos National Laboratory - Los Alamos, NM 87545, USA
2 Courant Institute of Mathematical Science - 251 Mercer St., New York, NY 10012, USA
(received 3 December 1998; accepted in final form 17 June 1999)
PACS. 05.45-a - Nonlinear dynamics and nonlinear dynamical systems.
PACS. 05.50+q - Lattice theory and statistics (Ising, Potts, etc.).
PACS. 63.10+a - Lattice dynamics: General theory.
The interplay between nonlinearity and disorder is studied in a discrete one-dimensional Schrödinger system. Using a two-point correlation function we demonstrate that the preferred state of the system comprises narrow intrinsic localized states corresponding to the intrinsic localized states of the ordered system. The essence of the interplay between disorder and nonlinearity is found to reside in the nucleation process of the localized states. We emphasize the role of different classes (focusing and defocusing) of nonlinearity in enhancing or suppressing localization induced by disorder.
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